On a denseness result for quasi-infinitely divisible distributions

2021/03/09 by Kutlu, Merve · 1 citation
#60E07 #60E10 (Primary) 60E05 (Secondary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.05393

Abstract

A probability distribution μ on ℝ^d is quasi-infinitely divisible if its characteristic function has the representation \widehatμ = \widehatμ₁/\widehatμ₂ with infinitely divisible distributions μ₁ and μ₂. In \cite[Thm. 4.1]lindner2018 it was shown that the class of quasi-infinitely divisible distributions on ℝ is dense in the class of distributions on ℝ with respect to weak convergence. In this paper, we show that the class of quasi-infinitely divisible distributions on ℝ^d is not dense in the class of distributions on ℝ^d with respect to weak convergence if d ≥ 2.

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• Denseness in total variation and the class of rational-infinitely divisible distributions

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